In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.

The article shows how two choices are possible whenever computing the geometric mean, and repetition of this process can in general yield 2-to-the power N different values when compounded first steps evaluation arithmetic-geometric mean. This happens not only simple AGM involved computation complete elliptic integral kind, but also analogous methods for incomplete integrals second kind.

The Analytic Hierarchy Process (AHP) is a popular methodology for group decision making. Individual judgments can be aggregated in several ways, with the most effective approach being the aggregation of individual judgments (AIJ) and Individual priorities (AIP). When the judgments are aggregated, regardless of whether AIJ or AIP are used, arithmetic and geometric means are selected by decision ...

The nervous system is the major target of the toxic effect of manganese (Mn) and its compounds. Nowadays, neurological diagnostics is directed towards early detection of symptoms and abortive forms, and the cases of serious damage of the nervous system are no longer reported. The aim of the present study was to assess the effects of manganese on the functions of the nervous system in workers ex...

In this paper a new aggregation operator for a class of LR Fuzzy Numbers i.e., Triangular Fuzzy Numbers (TFNs) in which the Land Rapex angles of the piecewise continuous linear membership function of the composite or resultant or aggregate TFN are the arithmetic means of the corresponding Land Rapex angles of the individual TFNs is proposed. The Land Rapex angles have been treated independently...

This paper presents the novel approach for pre-coding in multiple input and multiple output systems using arithmetic mean decomposition. This proposed decomposition scheme has low complexity than popular geometric mean decomposition. CORDIC based Givens rotation is used for making the channel matrix as bi-diagonal matrix and then 2x2 singular value decomposition and 2x2 arithmetic mean decompos...

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.

In this paper we introduce metric-based means for the space of positive-definite matrices. The mean associated with the Euclidean metric of the ambient space is the usual arithmetic mean. The mean associated with the Riemannian metric corresponds to the geometric mean. We discuss some invariance properties of the Riemannian mean and we use differential geometric tools to give a characterization...